Algebraic Thinking: possibilities of manifestation based on problem solving

Abstract

The present paper shows the result of a research that aimed to identify the manifestation of algebraic thinking in the students based on problem solving, and to understand in what way the teacher could interfere to develop such thinking. In order to reach that goal, we designed and applied a teaching plan to seventh grade students in two moments. First, the observation, when the teacher tried to understand whether just the students' engagement in problem solving would be enough to develop some algebraic thinking. Second, the mediation of the teacher through questions to guide the students' line of reasoning to one of the sides of algebraic thinking. As a result, it became clear that in order to arouse some algebraic thinking from problem solving, it is necessary to develop/adapt appropriate problems for each situation; the contextualization of generalization thinking from particular cases, observed through numbers, may trigger an increase of the students' ability to manipulate the unknown as if it was known, leading them to conceive mathematical objects, such as variable, unknown factor, constant, etc., which are necessary to understand and learn mathematical contents.